The White House and House of Representatives Speaker John Boehner's office held more negotiations on Monday on ways to break the US "fiscal cliff" stalemate, although neither side showed any public signs that they were ready to give ground.

The talks gained urgency after Republican Boehner met at the White House with President Barack Obama on Sunday, raising hopes of progress in averting the onset of tax increases and spending cuts that kicks in on January 1 unless Congress intervenes.

But while striking a more conciliatory tone, both sides kept to a familiar script in the weeks-long standoff. Obama renewed his call for higher tax rates for the richest Americans, which most Republicans oppose, while Republican leaders urged Obama to submit a new offer with specific spending cuts he would back.

Economists say going over the fiscal cliff could throw the US economy back into a recession.

On a road trip to Michigan to drum up support for his stance, Obama said he was willing to compromise on some things but not on his demand that Republicans support an increase in tax rates for the wealthiest 2 per cent of Americans.

"What you need is a package that keeps taxes where they are for middle-class families, we make some tough spending cuts on things that we don't need, and then we ask the wealthiest Americans to pay a slightly higher tax rate, and that's a principle I won't compromise on," Obama said during a visit to an auto plant in Redford, Michigan.

Boehner spokesman Michael Steel said Republicans were still waiting for the president to make a new offer that identifies the spending cuts he will make in the deficit-reduction negotiations.

"The Republican offer made last week remains the Republican offer," Steel said, adding the two sides were holding staff-level talks on Monday.

Boehner and the House Republican leadership submitted their terms for a deal to the White House last week, after Obama presented his opening proposal. Both sides seek to cut budget deficits by more than US$4 trillion ($4.8 trillion) over the next 10 years but differ drastically on how to get there.

Boehner and Republicans oppose letting any tax rates increase and prefer to find new revenues by closing loopholes and limiting deductions. Republicans also want deeper spending cuts than Obama has offered in entitlements like the Medicare and Medicaid healthcare programmes.

Democrats have insisted that tax rates for the richest must be nailed down before negotiating further on how to proceed with tax reform efforts or new spending cuts in entitlement programmes.

"I can only say that the president believes that a deal is possible," White House spokesman Jay Carney told reporters on the flight to Michigan. "But it requires acceptance and acknowledgement in a concrete way by Republicans that the top 2 per cent will see an increase in their rates."

Financial markets have calmed recently after a series of wild swings, when nearly every utterance from a politician about the looming budget crisis caused volatility in stock prices.

Polling shows most Americans would blame Republicans if the country goes over the cliff, and pressure has been building from some Republicans for Boehner to get an agreement quickly, even if it means tax hikes on the wealthiest.

Republican Senator Bob Corker of Tennessee called for a quick deal with the White House to allow an extension of the lower tax rates that have been in place for about a decade, except for the top two rates that Obama wants to raise.

"Right now there is no question in my mind the president has the slight upper hand in the negotiations," Corker said on CNBC on Monday.

He said there was support among Senate Republicans for taking that step so the fiscal cliff negotiations could then shift to focusing on how to restrain the growing costs of Medicare and other entitlement programmes.

"If you did it this week (agree to raising tax rates on the richest) you'd have the rest of this month to have the focus totally on entitlements," said Corker, who has a record of reaching out to Democrats on major bills.

More conservative Senate Republicans, most notably Senator Tom Coburn of Oklahoma, also have signalled a willingness to let tax rates rise on higher-income groups.

Erskine Bowles, co-chairman of the so-called Bowles-Simpson deficit reduction commission, said he thought chances were improving for a deal.

"I think the atmospherics are getting so much better. We have kind of gotten out of Kabuki theater and gone to dancing the tango," Bowles told CNBC on Monday. "Any time you start to tango you've got a chance."

Bowles said he did not expect the president to give in on his demand that taxes rise for the top 2 per cent of earners.

"I would almost guarantee that rates are going to go up for people in the top 2 per cent," he said.

US stocks edged higher on Monday but moves remained muted as investors looked for any signs of movement on the fiscal cliff front.

The S&P 500 index has nearly retraced the 5.3 per cent slide it suffered in the first seven sessions after the November 6 presidential election.

"The sentiment has definitely changed," said Andrew Wilkinson, chief economic strategist at Miller Tabak & Co in New York. "The market has become somewhat desensitized to headlines out of Washington because the fear of the economy hitting a wall in 2013 if we don't get a deal done has diminished."